Maths Higher Homework Pg 224 Qs 10, 13, 23 & 26 then to do
Past Paper for Completing the Square & Functions
2001 P1 Q4.
Given f(x) = x2 + 2x – 8 , express f(x) in the form (x + a)2 – b
2
2003 P1 Q2.
(a) Write f(x) = x2 + 6x + 11 in the form (x + a)2 + b
(b) Hence or otherwise sketch y = f(x)
2
2
2006 P1 Q8.
(a) Express 2x2 + 4x – 3 in the form a(x + b)2 + c
(b) Hence or otherwise sketch y = f(x)
2
2
2002 P1 Q7
(a) Express f(x) = x2 – 4x + 5 in the form (x + a)2 + b
3
(b) Write down the coordinates of the turning point.
1
(c) Find the range of values for which 10 – f(x) is positive.
1
2002 WD P1 Q9
The function f, defined on a suitable domain, is given by f(x)
= 3
(a) Find an expression for h(x), h(x) = f(f(x))
(b) Describe any restriction on the domain of h.
x+1
3
1
2003 P1 Q9
The function f(x)
= 1
&
g(x)
= 2x + 3
x–4
(a) Find an expression for h(x), where h(x) = f(g(x))
(b) Write down any restriction on the domain of h.
2
1
Maths Higher Homework Pg 224 Qs 10, 13, 23 & 26 then to do
Past Paper for Completing the Square & Functions
2006 P1 Q3
Two functions f and g are defined by f(x) = 2x + 3 and g(x) = 2x – 3, where x is a real number.
(a) Find an expression for
(i) f(g(x))
and (ii) g(f(x))
(b) Determine the least possible value of the product f(g(x)) x g(f(x))
3
2
2007 P1 Q3
Functions f and g are defined on suitable domains, f(x) = x2 + 1 and g(x) = 1 – 2x
(a) Find g(f(x))
(b) Find g(g(x))
2
2
y
2003P2 Q2
5
The graph of y = a sin (bx) + c is shown.
0
Determine the values of a, b and c.
π
-3
x
3
2003 P2 Q5
Function f has a minimum turning point at (0, -3) and a point of inflexion at (-4, 2)
(a) Sketch the graph of y = f(-x)
(b) On the same graph sketch y = 2f (-x )
2
2
2004 P1 Q4
The diagram shows the graph of y = g(x)
(a) Sketch the graph of y = –-g(x)
(b) On the same diagram sketch y = 3 – g(x)
2
2